Bell Work:

Write 2 formulas for the circumference of a circle.

Answer:

C = πD

C = 2πr

LESSON 40: AREA OF A CIRCLE

The area of a circle is related the the area of a square on the radius. The area of a circle is π times the area of a square on the radius. A formula for the area of a circle is

A = πr2

r

r

r2

The area of a circle is related to the area of a square on its radius. The area is greater than the area of three of these squares but less than the area of four such squares.

The area of the circle is π times the area of the square of the radius as we see from the formula A = πr.

2

Example:

A circular table in the library has a diameter of 6 feet. If four students sit around the table, then each student has about how many square feet of work area?

Answer:

A = 3.14(9 feet )

A ≈ 28.26 feet

2

2

Example:

Express the answers to (a) and (b) in terms of π.

a) What is the circumference of this circle?

b) What is the area of this circle?

6 inches

Answer:

a) Radius = 6 Diameter = 12

Circumference = 12π inches

b) Area = πr = π(6)

= 6π inches2

2 2

A sector of a circle is a portion of the interior of a circle enclosed by two radii and an arc which is part of the circle.

The angle formed by the radii, called a central angle, determines the fraction of the area of the circle the sector occupies.

Central Angle

Practice:

A lawn sprinkler waters a circular portion of a yard. The radius of the circular portion is 7 feet. Calculate the area of the yard watered by the sprinkler to the nearest square foot.

Answer:

22/7(7 feet)

= 22/7(49 feet )

≈154 feet

2

2

2

Practice:

What effect does doubling the diameter of a circle have on the area of the circle?

Answer:

Doubling the diameter doubles the radius. The radius is squared to calculate the area, so doubling the radius results in a circle with an area four times (2 ) as large.

2

Practice:

Find the area of the sector. Express in terms of π.

45°

6 cmM

R

S

Answer:

45°/360° = 1/8 of the circle

Area = πr

= π(4 cm)

= 16πcm

Area of sector = 1/8 16πcm

= 2πcm

2

2

2

2

2

Practice:

Find the area of the sector. Express in terms of π.

16 cm

Answer:

π(8 cm)

= 64πcm

Area of sector = ½(64πcm )

= 32πcm

2

2

2

2

HW: Lesson 40 #1-30